Partial Recovery in the Graph Alignment Problem

Georgina Hall () and Laurent Massoulié ()
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Georgina Hall: Decision Sciences, INSEAD, Fontainebleau 77300, France
Laurent Massoulié: DYOGENE, INRIA, Paris 75012, France

Operations Research, 2023, vol. 71, issue 1, 259-272

Abstract: In this paper, we consider the graph alignment problem, which is the problem of recovering, given two graphs, a one-to-one mapping between nodes that maximizes edge overlap. This problem can be viewed as a noisy version of the well-known graph isomorphism problem and appears in many applications, including social network deanonymization and cellular biology. Our focus here is on partial recovery ; that is, we look for a one-to-one mapping that is correct on a fraction of the nodes of the graph rather than on all of them, and we assume that the two input graphs to the problem are correlated Erdős–Rényi graphs of parameters ( n , q , s ). Our main contribution is then to give necessary and sufficient conditions on ( n , q , s ) under which partial recovery is possible with high probability as the number of nodes n goes to infinity. In particular, we show that it is possible to achieve partial recovery in the nqs = Θ ( 1 ) regime under certain additional assumptions.

Keywords: Machine Learning and Data Science; graph alignment; correlated Erdős–Rényi graphs; partial recovery (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:71:y:2023:i:1:p:259-272

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